A solution to the μ/Bμ problem in gauge mediation with hidden gauge symmetry

We propose a solution to the μ /Bμ problem in gauge-mediated SUSY breaking, which does not suffer from the SUSY CP problem and is consistent with the solution to the strong CP problem. The model is based on Z ₃-invariant NMSSM with additional vector-like matter charged under a hidden gauge group as well as the standard model gauge groups. The dynamical scale of the hidden gauge symmetry is set to be around 1 0 GeV. We show that this simple extension of the NMSSM resolves the domain wall problem and the μ /Bμ problem without a dangerous CP angle. The relative sign among gaugino masses and the μ parameter can be preferable in terms of the muon anomalous magnetic moment. We also discuss cosmological issues of this model, especially the effects of long-lived particles in the hidden gauge sector. The hidden glueball may cause a late-time entropy production, which opens up a possibility that the light gravitino can be a dominant component of dark matter while leptogenesis scenarios work successfully. There is a region where the electroweak symmetry is successfully broken with - 10 TeV stops, and the Higgs mass of ∼ 1 25 GeV can be explained.